### Abstract

Motivated by the recent Kitaev's K-theory analysis of topological insulators and superconductors, we adopt the same framework to study the topological phase structure of Jackiw-Rebbi model in 3+1 dimensions. According to the K-theory analysis based on the properties of the charge conjugation and time reversal symmetries, we classify the topological phases of the model. In particular, we find that there exist Z Majorana zero-modes hosted by the hedgehogs/t'Hooft-Polyakov monopoles, if the model has a T ^{2} = 1 time reversal symmetry. Guided by the K-theory results, we then explicitly show that a single Majorana zero mode solution exists for the SU(2) doublet fermions in some co- dimensional one planes of the mass parameter space. It turns out we can see the existence of none or a single zero mode when the fermion doublet is only two. We then take a step further to consider four-fermion case and find there can be zero, one or two normalizable zero mode in some particular choices of mass matrices. Our results also indicate that a single normalizable Majorana zero mode can be compatible with the cancellation of SU(2) Witten anomaly.

Original language | English |
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Article number | 74 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2012 Jan 1 |

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### Keywords

- Anyons
- Nonperturbative Effects
- Solitons Monopoles and Instantons

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2012*(12), [74]. https://doi.org/10.1007/JHEP12(2012)074